And does she require her husband's permission for that if she is a salary earner?
Well i think its OK to help your family, but do not over-do it. I mean, don't do it at the expense of your own household and their hapiness. I know some women who would want to help their brothers even when they know their household-expenses cannot affort it.
They think its their husband's loss but at the end of the day it hurts all parties involved. Atimes it results to hidden enemity between the in-laws (the husband and the brohers of the lady, more unlucky situations will now draw the lady's mum into the mess)

Something that could have been prevented if the lady was being a wife and mother first

And does she require her husband's permission for that if she is a salary earner?
To some extent, yes she does. Its not only on paper you guys agree to be "one", its for a living. When huge decisions are to be made, they should both be in agreement, even though its the lady's salary.
Aren't they supposed to be taking care of the family together?
Shouldn't they be more of a couple than single individually minded?
Would the lady appreciate it if the guy shipped half of his earnings to his birth family.
If its a chicken-change to buy bisciuts and chocolates, thats a differnt one but
When you're married, in my opinion your immediate family becomes your first priority and planning spot
